Dual-component phase reconstruction in double Lloyd’s mirror profilometry

Abstract

A double Lloyd’s mirror configuration is demonstrated for compact optical profilometry using optically superimposed fringe projection and two-dimensional continuous wavelet transform (2D CWT)-based separation. The system generates two nearly orthogonal fringe families in a single object frame, allowing the horizontal and vertical components to be separated and used as complementary phase-information channels. After reference correction, the component-wise phase maps are converted into height distributions and combined to reconstruct the final surface profile. The method was evaluated on a smooth half-egg-shaped benchmark object by comparing the superimposed-fringe reconstruction with a conventional single-fringe Lloyd’s mirror reconstruction and the CAD reference. For the selected half-egg cross-section, using both fringe components reduced the RMSE from 0.204 mm to 0.098 mm and the MAE from 0.142 mm to 0.072 mm relative to the conventional single-fringe reconstruction. The method was further applied to a star-shaped object with curved boundaries and tip regions, where digital caliper measurements were consistent with the reconstructed height distribution, including the observed central height variation. These results indicate that double Lloyd’s mirror profilometry combined with 2D CWT separation provides a compact all-optical route for exploiting horizontal and vertical fringe information in full-field three-dimensional surface reconstruction.